I have succesfuly shared data between my two accounts untill I ran them on two separate computers. It worked either by targeting other character or by typing its nickname.
Once I bought new computer and run both WoWs on in - sharing content stopped working.
With 'Always authorize requests' When I send request, the receiver doesn't receive it.
When I make the requests as "Ask for authorization", the receiver in fact gets the Authorization request, but after allowing it nothing happens except Error message in chat: Messagebox handler not defined.

Once I run both accounts again on separate machines - Data sharing works again miraculously.